Interior-point algorithms for semi-infinite programming

In order to study the behavior of interior-point methods on very large-scale linear programming problems, the paper considers the application of such methods to continuous semi-infinite linear programming problems in both primal and dual form. By considering different discretizations of such problems it is led to a certain invariance property for (finite-dimensional) interior-point methods. The paper finds that while many methods are invariant, several, including all those with the currently best complexity bound, are not. It then devises natural extensions of invariant methods to the semi-infinite case. The present motivation comes from the belief that for a method to work well on large-scale linear programming problems, it should be effective on fine discretizations of a semi-infinite problem and it should have a natural extension to the limiting semi-infinite case.